Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Strong-field control by reverse engineering

Attila Tóth, András Csehi

Published Dec 2, 2021• 11 citations
Publisher

Abstract

Based on the idea of reverse engineering, we design an optimal laser pulse to control strong-field multiphoton atomic transitions. Starting from the time-dependent Schr\"odinger equation of the full system, we adiabatically eliminate the nonessential states and apply the rotating-wave approximation to arrive at an effective two-state representation that involves dynamic Stark shifts and multiphoton coupling. Solving this equation inversely for the field, we obtain an analytical laser pulse shape that is expected to induce the full system's evolution according to user-defined quantum pathways. In our procedure, the amplitude and phase of the laser pulse are engineered such that the dynamically shifted electronic states are resonantly coupled during the action of the pulse at each moment of time. As a result, the driven system evolves from an arbitrary initial population distribution to any desired final quantum state superposition at a predefined rate. The proposed scheme is demonstrated using the example of the $3s\ensuremath{\rightarrow}4s$ two-photon transition of atomic sodium. By solving the time-dependent Schr\"odinger equation of the single-active electron with two different methods, either propagating time-dependent coefficients of many field-free states or directly propagating the three-dimensional electronic wave packet on a grid, we demonstrate the robustness as well as the limitations of the presented reverse engineering scheme.

DOI
10.1103/physreva.104.063102

Related papers

Reverse-engineering control of the population and phase dynamics of strongly driven open systems

András Csehi

We apply reverse engineering to design laser pulse shapes for controlling the time evolution of strong-field transitions under environmental effects. Our effective two-state representation of the full quantum system involves dynamic Stark shifts and multiphoton Rabi frequency. Furthermore, the environment is modeled with dephasing and dissipative terms. Solving the master equation of the two-level density matrix inversely for the field, we obtain quasianalytic laser pulse shapes that simultaneously drive the populations and relative phase according to user-defined quantum pathways. The validity of the proposed scheme is demonstrated with the example of the $3s\ensuremath{\rightarrow}\ensuremath{\rightarrow}4s$ two-photon transition of atomic sodium by solving the master equation of the multilevel system that incorporates effects beyond the adiabatic elimination and the rotating wave approximation. Due to the open character of the system, the proposed control is not always possible. We explore these situations and point out the conditions for creating steady states with large coherence.

Physical Review A•Sep 26, 2025•1 citation

Effective pulse reverse-engineering for strong field–matter interaction

Du Ran, Bin Zhang, Ye‐Hong Chen +5 more

In this Letter, we propose a scheme to control the evolution of a two-level quantum system in the strong-coupling regime, based on the idea of reverse engineering. A coherent control field is designed to drive the system along a user-predefined evolution trajectory without utilizing the rotating-wave approximation. As concrete examples, we show that complete population inversion, an equally weighted coherent superposition, and even oscillation-like dynamics can be achieved. Since there are no limitations on the coupling strength between the control field and matter, the scheme is attractive for applications such as accelerating desired system dynamics and fast quantum information processing.

arXiv:2003.01828•Optics Letters•May 20, 2020•17 citations

Pulse reverse engineering for controlling two-level quantum systems

Du Ran, Wu‐Jiang Shan, Zhi‐Cheng Shi +3 more

In this paper, based on the idea of reverse engineering, we propose a scheme to find analytical expressions of a laser pulse that allows for controlling the evolution of two-level systems as desired, regardless of the time-dependent phase of the system. The pulse relates to particular functions that predefine the evolution of a system. For illustration, we present concrete examples of driving the system from an arbitrary initial state to a final state along the user-prescribed particular way in both closed and open quantum systems. Simulation results indicate that the desired evolutionary path is accurately obtained when the rotating wave approximation (RWA) is satisfied. Most importantly, the scheme allows us to maintain system coherence and populations even in the presence of certain dephasing and thermal noises. Thus it may naturally find applications in quantum computing and quantum memories.

Physical Review A•Feb 14, 2020•24 citations

Control of the populations and phases of two-level quantum systems by a single frequency-chirped laser pulse

András Csehi

Abstract We present an analytical electric field expression to simultaneously control the population and phase dynamics of two-level quantum systems. The presented electric field is obtained by a reverse engineering technique after the desired population and phase evolution pathways of the system have been specified. Upon application of this laser field, the system is driven from an arbitrary quantum state superposition to the desired population distribution; meanwhile the phase of one of the states proceeds according to a predefined path. The robustness of the engineered electric field is demonstrated by numerical simulations on the example of the 3s → 3p transition of atomic sodium. Furthermore, the limitations of the presented technique, which arise due to the application of the rotating wave approximation, are thoroughly analyzed and discussed.

Journal of Physics B Atomic Molecular and Optical Physics•Aug 19, 2019•16 citations

Role of dynamic Stark shifts in strong-field excitation and subsequent ionization

Attila Tóth, S. Borbély, Yueming Zhou +1 more

The energy levels of atoms and molecules exposed to intense, short, high-frequency laser pulses undergo time-dependent distortion known as dynamic Stark shift (DSS). These level shifts are induced by the coupling with nonresonant (nonessential) states and follow the temporal intensity profile of the laser pulse. Owing to the different DSSs of the individual atomic levels, transient resonance suppressions and enhancements significantly modify the multiphoton ionization pathway, leaving clear fingerprints (asymmetry, splitting, and shifting) in the energy spectrum of emitted photoelectrons. Here we investigate this phenomenon by solving the time-dependent Schr\"odinger equation of the valence electron of Na and Li in increasing levels of complexity: (i) developing minimal models for two-photon transition and ($2+1$)-photon ionization, (ii) applying a spectral method without continuum-continuum couplings, and (iii) propagating the electron wave packet on a large spatial grid accounting for all possible couplings. We show that appropriately detuned transform limited pulses provide a high level of control in strong-field excitation, when the atomic levels are dynamically shifted. Furthermore, we demonstrate the role of DSSs in the multipeak structure of the Autler-Townes doublet, found when several Rabi oscillations are induced during the strong-field resonant ionization.

Physical Review A•May 1, 2023•24 citations

Coherent control of strong field multiphoton absorption in the presence of dynamic Stark shifts

Carlos A Trallero-Herrero, David Cardoza, Thomas C. Weinacht +1 more

We show that coherent control of multiphoton transitions is possible in the strong field limit, even in the presence of large dynamic Stark shifts. By tailoring the phase of an ultrafast laser pulse, one can compensate for the dynamic Stark shift during the atom-field interaction to achieve efficient population transfer in two-photon absorption. Numerical simulations for atomic sodium reveal efficient population transfer from the $\ensuremath{\mid}3s⟩$ ground state to the $\ensuremath{\mid}4s⟩$ excited state using an appropriately shaped ultrafast laser pulse. The theory and simulations provide insight into coherent control of more complicated multiphoton processes.

Physical Review A•Jan 28, 2005•70 citations
Based on the idea of reverse engineering, we design an optimal laser pulse to control strong-field multiphoton atomic transitions. Starting from the time-dependent Schr"odinger equation of the full system, we adiabatically eliminate the nonessential states and apply the rotating-wave approximation to arrive at an effective two-state representation that involves dynamic Stark shifts and multiphoton coupling. Solving this equation inversely for the field, we obtain an analytical laser pulse shape that is expected to induce the full system's evolution according to user-defined quantum pathways. In our procedure, the amplitude and phase of the laser pulse are engineered such that the dynamically shifted electronic states are resonantly coupled during the action of the pulse at each moment of time. As a result, the driven system evolves from an arbitrary initial population distribution to any desired final quantum state superposition at a predefined rate. The proposed scheme is demonstrated using the example of the 3s\ensuremath→4s3s\ensuremath{\rightarrow}4s3s\ensuremath→4s two-photon transition of atomic sodium. By solving the time-dependent Schr"odinger equation of the single-active electron with two different methods, either propagating time-dependent coefficients of many field-free states or directly propagating the three-dimensional electronic wave packet on a grid, we demonstrate the robustness as well as the limitations of the presented reverse engineering scheme.
We apply reverse engineering to design laser pulse shapes for controlling the time evolution of strong-field transitions under environmental effects. Our effective two-state representation of the full quantum system involves dynamic Stark shifts and multiphoton Rabi frequency. Furthermore, the environment is modeled with dephasing and dissipative terms. Solving the master equation of the two-level density matrix inversely for the field, we obtain quasianalytic laser pulse shapes that simultaneously drive the populations and relative phase according to user-defined quantum pathways. The validity of the proposed scheme is demonstrated with the example of the $3s\ensuremath{\rightarrow}\ensuremath{\rightarrow}4s$ two-photon transition of atomic sodium by solving the master equation of the multilevel system that incorporates effects beyond the adiabatic elimination and the rotating wave approximation. Due to the open character of the system, the proposed control is not always possible. We explore these situations and point out the conditions for creating steady states with large coherence.
In this Letter, we propose a scheme to control the evolution of a two-level quantum system in the strong-coupling regime, based on the idea of reverse engineering. A coherent control field is designed to drive the system along a user-predefined evolution trajectory without utilizing the rotating-wave approximation. As concrete examples, we show that complete population inversion, an equally weighted coherent superposition, and even oscillation-like dynamics can be achieved. Since there are no limitations on the coupling strength between the control field and matter, the scheme is attractive for applications such as accelerating desired system dynamics and fast quantum information processing.
In this paper, based on the idea of reverse engineering, we propose a scheme to find analytical expressions of a laser pulse that allows for controlling the evolution of two-level systems as desired, regardless of the time-dependent phase of the system. The pulse relates to particular functions that predefine the evolution of a system. For illustration, we present concrete examples of driving the system from an arbitrary initial state to a final state along the user-prescribed particular way in both closed and open quantum systems. Simulation results indicate that the desired evolutionary path is accurately obtained when the rotating wave approximation (RWA) is satisfied. Most importantly, the scheme allows us to maintain system coherence and populations even in the presence of certain dephasing and thermal noises. Thus it may naturally find applications in quantum computing and quantum memories.
Abstract We present an analytical electric field expression to simultaneously control the population and phase dynamics of two-level quantum systems. The presented electric field is obtained by a reverse engineering technique after the desired population and phase evolution pathways of the system have been specified. Upon application of this laser field, the system is driven from an arbitrary quantum state superposition to the desired population distribution; meanwhile the phase of one of the states proceeds according to a predefined path. The robustness of the engineered electric field is demonstrated by numerical simulations on the example of the 3s → 3p transition of atomic sodium. Furthermore, the limitations of the presented technique, which arise due to the application of the rotating wave approximation, are thoroughly analyzed and discussed.
The energy levels of atoms and molecules exposed to intense, short, high-frequency laser pulses undergo time-dependent distortion known as dynamic Stark shift (DSS). These level shifts are induced by the coupling with nonresonant (nonessential) states and follow the temporal intensity profile of the laser pulse. Owing to the different DSSs of the individual atomic levels, transient resonance suppressions and enhancements significantly modify the multiphoton ionization pathway, leaving clear fingerprints (asymmetry, splitting, and shifting) in the energy spectrum of emitted photoelectrons. Here we investigate this phenomenon by solving the time-dependent Schr\"odinger equation of the valence electron of Na and Li in increasing levels of complexity: (i) developing minimal models for two-photon transition and (2+12+12+1)-photon ionization, (ii) applying a spectral method without continuum-continuum couplings, and (iii) propagating the electron wave packet on a large spatial grid accounting for all possible couplings. We show that appropriately detuned transform limited pulses provide a high level of control in strong-field excitation, when the atomic levels are dynamically shifted. Furthermore, we demonstrate the role of DSSs in the multipeak structure of the Autler-Townes doublet, found when several Rabi oscillations are induced during the strong-field resonant ionization.
We show that coherent control of multiphoton transitions is possible in the strong field limit, even in the presence of large dynamic Stark shifts. By tailoring the phase of an ultrafast laser pulse, one can compensate for the dynamic Stark shift during the atom-field interaction to achieve efficient population transfer in two-photon absorption. Numerical simulations for atomic sodium reveal efficient population transfer from the $\ensuremath{\mid}3s⟩$ ground state to the $\ensuremath{\mid}4s⟩$ excited state using an appropriately shaped ultrafast laser pulse. The theory and simulations provide insight into coherent control of more complicated multiphoton processes.